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Branching Time and Abstraction in Bisimulation Semantics
 Journal of the ACM
, 1996
"... Abstract. In comparative concurrency semantics, one usually distinguishes between linear time and branching time semantic equivalences. Milner’s notion of ohsen~ation equirlalence is often mentioned as the standard example of a branching time equivalence. In this paper we investigate whether observa ..."
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Cited by 323 (17 self)
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Abstract. In comparative concurrency semantics, one usually distinguishes between linear time and branching time semantic equivalences. Milner’s notion of ohsen~ation equirlalence is often mentioned as the standard example of a branching time equivalence. In this paper we investigate whether observation equivalence really does respect the branching structure of processes, and find that in the presence of the unobservable action 7 of CCS this is not the case. Therefore, the notion of branching hisimulation equivalence is introduced which strongly preserves the branching structure of processes, in the sense that it preserves computations together with the potentials in all intermediate states that are passed through, even if silent moves are involved. On closed KSterms branching bisimulation congruence can be completely axiomatized by the single axiom scheme: a.(7.(y + z) + y) = a.(y + z) (where a ranges over all actions) and the usual laws for strong congruence. WC also establish that for sequential processes observation equivalence is not preserved under refinement of actions, whereas branching bisimulation is. For a large class of processes, it turns out that branching bisimulation and observation equivalence are the same. As far as we know, all protocols that have been verified in the setting of observation equivalence happen to fit in this class, and hence are also valid in the stronger setting of branching hisimulation equivalence.
On the Bisimulation Proof Method
 JOURNAL OF MATHEMATICAL STRUCTURES IN COMPUTER SCIENCE
, 1994
"... The most popular method for establishing bisimilarities among processes is to exhibit bisimulation relations. By definition, R is a bisimulation relation if R progresses to R itself, i.e., pairs of processes in R can match each other's actions and their derivatives are again in R. We study gen ..."
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Cited by 103 (6 self)
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The most popular method for establishing bisimilarities among processes is to exhibit bisimulation relations. By definition, R is a bisimulation relation if R progresses to R itself, i.e., pairs of processes in R can match each other's actions and their derivatives are again in R. We study generalisations of the method aimed at reducing the size of the relations to exhibit and hence relieving the proof work needed to establish bisimilarity results. We allow a relation R to progress to a different relation F(R), where F is a function on relations. Functions which can be safely used in this way (i.e., such that if R progresses to F(R), then R only includes pairs of bisimilar processes) are sound. We give a simple condition which ensures soundness. We show that the class of sound functions contains nontrivial functions and we study the closure properties of the class w.r.t. various important function constructors, like composition, union and iteration. These properties allow us to cons...
Modal and Temporal Logics for Processes
, 1996
"... this paper have been presented at the 4th European Summer School in Logic, Language and Information, University of Essex, 1992; at the Tempus Summer School for Algebraic and Categorical Methods in Computer Science, Masaryk University, Brno, 1993; and the Summer School in Logic Methods in Concurrency ..."
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Cited by 91 (2 self)
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this paper have been presented at the 4th European Summer School in Logic, Language and Information, University of Essex, 1992; at the Tempus Summer School for Algebraic and Categorical Methods in Computer Science, Masaryk University, Brno, 1993; and the Summer School in Logic Methods in Concurrency, Aarhus University, 1993. I would like to thank the organisers and the participants of these summer schools, and of the Banff higher order workshop. I would also like to thank Julian Bradfield for use of his Tex tree constructor for building derivation trees and Carron Kirkwood, Faron Moller, Perdita Stevens and David Walker for comments on earlier drafts.
Verification on Infinite Structures
, 2000
"... In this chapter, we present a hierarchy of infinitestate systems based on the primitive operations of sequential and parallel composition; the hierarchy includes a variety of commonlystudied classes of systems such as contextfree and pushdown automata, and Petri net processes. We then examine the ..."
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Cited by 91 (2 self)
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In this chapter, we present a hierarchy of infinitestate systems based on the primitive operations of sequential and parallel composition; the hierarchy includes a variety of commonlystudied classes of systems such as contextfree and pushdown automata, and Petri net processes. We then examine the equivalence and regularity checking problems for these classes, with special emphasis on bisimulation equivalence, stressing the structural techniques which have been devised for solving these problems. Finally, we explore the model checking problem over these classes with respect to various linear and branchingtime temporal logics.
Petri Nets, Commutative ContextFree Grammars, and Basic Parallel Processes
, 1997
"... . The paper provides a structural characterisation of the reachable markings of Petri nets in which every transition has exactly one input place. As a corollary, the reachability problem for this class is proved to be NPcomplete. Further consequences are: the uniform word problem for commutative co ..."
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Cited by 68 (6 self)
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. The paper provides a structural characterisation of the reachable markings of Petri nets in which every transition has exactly one input place. As a corollary, the reachability problem for this class is proved to be NPcomplete. Further consequences are: the uniform word problem for commutative contextfree grammars is NPcomplete; weakbisimilarity is semidecidable for Basic Parallel Processes. Keywords: Petri nets, Commutative Contextfree Grammars, Basic Parallel Processes, Weak bisimilarity. 1. Introduction The reachability problem plays a central role in Petri net theory, and has been studied in numerous papers (see [5] for a comprehensive list of references). In the first part of this paper we study it for the nets in which every transition needs exactly one token to occur. Following [8], we call them communicationfree nets, because no cooperation between places is needed in order to fire a transition; every transition is activated by one single token, and the tokens may flow...
Undecidable Verification Problems for Programs with Unreliable Channels
 Information and Computation
, 1994
"... We consider the verification of a particular class of infinitestate systems, namely systems consisting of finitestate processes that communicate via unbounded lossy FIFO channels. This class is able to model e.g. link protocols such as the Alternating Bit Protocol and HDLC. In an earlier paper, we ..."
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Cited by 67 (13 self)
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We consider the verification of a particular class of infinitestate systems, namely systems consisting of finitestate processes that communicate via unbounded lossy FIFO channels. This class is able to model e.g. link protocols such as the Alternating Bit Protocol and HDLC. In an earlier paper, we showed that the problems of checking reachability, safety properties, and eventuality properties are decidable for this class of systems. In this paper, we show that the following problems are undecidable, namely ffl The model checking problem in propositional temporal logics such as Propositional Linear Time Temporal Logic (PTL) and Computation Tree Logic (CTL). ffl The problem of deciding eventuality properties with fair channels: do all computations eventually reach a given set of states if the unreliable channels satisfy fairness assumptions. The results are obtained through a reduction from a variant of Post's Correspondence Problem. This research report is a revised and extended ...
Infinite Results
, 1996
"... Recently there has been a spurt of activity in concurrency theory centred on the analysis of infinitestate systems. Much of this work stems from a task dedicated to the study in the recentlyconcluded ESPRIT BRA Concur2, and much of it has subsequently appeared in the proceedings of the annual CO ..."
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Cited by 66 (5 self)
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Recently there has been a spurt of activity in concurrency theory centred on the analysis of infinitestate systems. Much of this work stems from a task dedicated to the study in the recentlyconcluded ESPRIT BRA Concur2, and much of it has subsequently appeared in the proceedings of the annual CONCUR conference. In this paper, we present an overview of various results obtained regarding expressivity, decidability, and complexity, focussing on the various techniques exploited in each case.
Decidability of Model Checking for InfiniteState Concurrent Systems
 Acta Informatica
"... We study the decidability of the model checking problem for linear and branching time logics, and two models of concurrent computation, namely Petri nets and Basic Parallel Processes. 1 Introduction Most techniques for the verification of concurrent systems proceed by an exhaustive traversal of the ..."
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Cited by 65 (1 self)
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We study the decidability of the model checking problem for linear and branching time logics, and two models of concurrent computation, namely Petri nets and Basic Parallel Processes. 1 Introduction Most techniques for the verification of concurrent systems proceed by an exhaustive traversal of the state space. Therefore, they are inherently incapable of considering systems with infinitely many states. Recently, some new methods have been developed in order to at least palliate this problem. Using them, several verification problems for some restricted infinitestate models have been shown to be decidable. These results can be classified into those showing the decidability of equivalence relations [8, 9, 24, 26], and those showing the decidability of model checking for different modal and temporal logics. In this paper, we contribute to this second group. The model checking problem has been studied so far for three infinitestate models: contextfree processes, pushdown processes, and...
Undecidability of Bisimilarity for Petri Nets and Some Related Problems
, 1995
"... The main result shows the undecidability of (strong) bisimilarity for labelled (place / transition) Petri nets. The technique of the proof applies to the language (or trace) equivalence and the reachability set equality as well, which yields stronger versions with simpler proofs of already known ..."
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Cited by 59 (3 self)
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The main result shows the undecidability of (strong) bisimilarity for labelled (place / transition) Petri nets. The technique of the proof applies to the language (or trace) equivalence and the reachability set equality as well, which yields stronger versions with simpler proofs of already known results. The paper also contains two decidability results. One concerns the Petri nets which are deterministic up to bisimilarity, the other concerns semilinear bisimulations and extends the result of [4] for Basic Parallel Processes. 1 Introduction The topic of the paper belongs to an interesting area in the theory of parallelism and concurrency, namely to the area of decidability questions for behavioural equivalences in various classes of (models of) processes. These questions are among the rst ones to ask when developing automated verication methods, for example. There is a large amount of equivalences in the literature (cf. e.g. [9]), nevertheless some of them are felt to be mor...